Abstract
In the previous paper by Alt et al (1984 Indiana Univ. Math. J. 33 367–91), the existence of the symmetric plane flows of two fluids with two free boundaries has been established by variational approach. However, the uniqueness of the two-phase fluids with two free boundaries is an unsolved problem. In the present paper, we will deal with the uniqueness of the two-phase fluids. In addition, if we assume that the two nozzles both converge, we shall show the monotonicity of the two free boundaries of the incompressible two-phase fluids issuing from these two nozzles.
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